Numerical Analysis/Computational Methods

(b) Show that, for x; = cos(j7), n II(x xk) 2-1682 19091() k=0 n W;= and 2n-1(x - 1;) 1/ II (x; xk) lim TT (22 1)Un-1(2) k=0,k+j sin(n arccos x) Here Un-1(2) is the Chebyshev polynomial of the second kind of degree n - 1. sin(arccos x) (c) Use L'Hospital's Rule to evaluate the limit in (b) and derive the expressions in (??). (b) Show that, for x; = cos(j7), n II(x xk) 2-1682 19091() k=0 n W;= and 2n-1(x - 1;) 1/ II (x; xk) lim TT (22 1)Un-1(2) k=0,k+j sin(n arccos x) Here Un-1(2) is the Chebyshev polynomial of the second kind of degree n - 1. sin(arccos x) (c) Use L'Hospital's Rule to evaluate the limit in (b) and derive the expressions in (??)